for a sample \(\left(\lambda _C^{(i)}\right)_{i = 1, ..., n} \sim {P}(\lambda _C)\) . \(\hat{m} \left(\lambda _S, \lambda _C^{(i)}\right)\)  represents the marginal effect of \(\lambda _S\)  for one specific instance \(i\) .
Individual conditional expectation (ICE) curves [1]} visualize the marginal effect of the \(i\) -th observation by plotting the value of \(\hat{m} \left(\lambda _S, \lambda _C^{(i)}\right)\)  against \(\lambda _S\)  for a set of grid pointsGrid points are typically chosen as an equidistant grid or sampled from \({P}(\lambda _S)\) . The granularity \(G\)  is chosen by the user. For categorical features, the granularity typically corresponds to the number of categories. \(\lambda _S^{(g)}\in \Lambda _S\) , \(g \in \lbrace 1, ..., G\rbrace \) .
Analogously, the PDP visualizes \(\hat{c}_{S}(\lambda _S)\)  against the grid points.
Following from Eq. REF , the PDP visualizes the average over all ICE curves.
In HPO, the marginal predicted performance is a related concept. Instead of approximating the integral via Monte Carlo, the integral over \(\hat{c}\)  is computed exactly. [2]} propose an efficient approach to compute this integral for random forest surrogate models.
